Question: Hadassah bowls a strike on $60\%$ of the frames she bowls. Let $F$ be the number of frames Hadassah bowls until she bowls a strike. Assume the results of each frame are independent. Find the probability that it takes Hadassah less than $3$ frames to bowl her first strike. You may round your answer to the nearest hundredth. $P(F<3)=$
Answer: Without a fancy calculator On each frame: $P({\text{strike}})=0.6$ $P(\text{not}})=0.4$ If it takes Hadassah less than $3$ frames to bowl her first strike, here are the possible sequences of frames: strike not, strike We can find the probability of each sequence and add those probabilities together. $\begin{aligned} P({\text{strike}})&=0.6\\\\\\ P(\text{not}}, {\text{strike}})&=(0.4})({0.6})\\\\&=0.24\\\\\\ P(F<3)&=0.6+0.24\\\\&=0.84 \end{aligned}$ [Is there another way?] $P(F<3)=0.84$